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Microscopic study of edges of fractional quantum Hall states

English title Microscopic study of edges of fractional quantum Hall states
Applicant Morf Rudolf H.
Number 116657
Funding scheme Project funding
Research institution Paul Scherrer Institut
Institution of higher education Paul Scherrer Institute - PSI
Main discipline Theoretical Physics
Start/End 01.04.2007 - 31.10.2007
Approved amount 27'881.00
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Keywords (9)

Pfaffian State; Fractional quantum Hall effect; Quantum Computation; Topological Order; Edge States; edge currents; microscopic calculation; non-abelian statistics; ground state degeneracy

Lay Summary (English)

Lay summary
The theoretical understanding of fractional quantum Hall (FQH) states along the main sequence of filling fractions nu = 1/3, 2/5, 3/7,...,n/(2n + 1) is quite advanced concerning their bulk properties, e.g. excitation energies and structure of charged excitations. FQH states are characterized by finite energy gaps leading to their incompressibility. At the boundaries of FQH states chiral (edge) currents form, whose properties have been analyzed within phenomenological theories (conformal field theory). Their microscopic structure has however not been thoroughly analyzed and important questions concerning the structure of edge states remain unanswered. In particular, the edge structure of the fully spin polarized states at filling nu= 2/3 and 2/5, e.g. the number of edge currents, has remained controversial. In this PhD thesis, the edge structure of these states will be studied microscopically by means of exact diagonalisation of the Hamiltonian for systems of a few (up to 26) electrons. In particular, we wish to understand the effect of squeezing of the electron system as is achieved in experiment by applying gate voltages to electrodes that allow the formation of a quantum point contact. By such squeezing, phase transitions can be induced in which edge channels will be reflected at the "point contact" as will be explained in detail in this proposal.
Another topic has become very interesting and challenging in this area of physics: the nature of the still enigmatic nu = 5/2 state. If it does indeed belong to the class of Pfaffian states as many people hope, it can be used for quantum computation in a particularly attractive way, as its excitations are subject to non-abelian statistics. These help protect the quantum correlations within the system from local perturbations, e.g. thermal fluctuations. We have decided to embark on a detailed study of the properties of the 5/2 state, and in particular to investigate if the hope that it does belong to the Pfaffian class is justified. The work on the study of edges will be taken up again after completion of this investigation.
It turns out that the theoretical and numerical methods we have developed for the study of the non-abelian character of the 5/2 state will simplify the study of edges of the ordinary fractional states in an important way, thus helping our original project.
Direct link to Lay Summary Last update: 21.02.2013

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Associated projects

Number Title Start Funding scheme
100329 Microscopic study of edges of fractional quantum Hall states 01.11.2003 Project funding